Corso di laurea in Chimica e Tecnologie Chimiche

Mathematics, and in particularl linear algebra and analysis; physics (mechanics in particular) and electromagnetism.

Later physical-chemical courses; all courses that have some kind of reference to the electronic structure of atoms, molecules and solids, and to spectroscopy.

Provide formal and conceptual tools for understanding the chemical complexity; opening to a quantum-mechanical approach to chemistry.

Familiarity with the periodic system, basic concepts related to the electronic structure of the systems of chemical interest (atoms, molecules, solids, liquids, spectroscopy.

The course provides an introduction to the atomic and molecular quantum theories. It covers the fundamentals of quantum mechanics with its postulates and theorems. We illustrate the reference models (the free particle, the molecule that rotates or vibrates, the hydrogen atom) and techniques (variational method and perturbation theory, group theory). The electronic structure of the molecules (with references to the atomic states and the condensed state) and the information that can be drawn from the rotational and vibrational spectroscopy are the primary focus of the course. The full program is as follows:

1. Notes on mathematics and linear algebra.
2. Group Theory. Symmetry elements and operations, order of a group. Classes. Multiplication table. Bases and representations. Character tables and their vector interpretation. Reducible Representations (RR) and their decomposition. Symmetry of the translation, rotation and vibration motions of molecules. IR and Raman vibrational activity.
3. Introduction to quantum mechanics (QM). The inadequacy of classical mechanics at the atomic scale: black body; photoelectric effect; electron diffraction and wave/particle dualism; atomic emission spectra. The spectrum of the hydrogen atom. Heisenberg's uncertainty principle.
4. The quantum wave equation and the Schröedinger equation (EdS). EdS as an eigenvalue problem. Postulates of quantum mechanics and their meaning. Wavefunction and probability. Wavefunction requirements.
5. QM applied to simple systems: (a) particle in the box (one- and three-dimensional); (b) the harmonic oscillator (and the vibrations of the molecules); (c) the rigid rotator.
6. Approximate methods and perturbation theory. Examples for anharmonic oscillator and H and He atoms. The variational method (linear and non-linear): connections with linear algebra and the use of the calculator. The LCAO method and the H2 molecule.
7. Atomic structure. The hydrogen atom (short discussion): EdS; separation of variables; explicit solution of the part in φ. Eigenvalues ​​and eigenvectors, degeneracy and graphical representation. Nodes and nodal surfaces. Atomic orbitals (AO). Angular momentum and connection with the rigid rotator. Meaning of the quantum numbers l and m. The Spin. Level scheme and spectroscopy of the H atom. Representation of wave functions. Polyelectronic atoms: aufbau and construction of the periodic system. Configurations, states and termination symbols. The antisymmetry principle and the Slater determinant.
8. The H2+ molecule. Setting the EdS and Born-Oppenheimer approximation. The LCAO method and the molecular orbitals of H2+.
9. Simple diatomic homo- (H2, Li2, B2, C2, N2, O2, F2) and hetero-nuclear (CO, HF and NaCl) molecules. Hybridization: methane, ethylene and acetylene. Hückel's method. Conjugated systems and electronic delocalization. Aromatic molecules: benzene.
10. The matter-radiation interaction. Notes on the theory of time-dependent perturbations. Field-dipole interaction and magnetic spectroscopies. Absorption and emission probabilities and Einstein coefficients. Notes on LASERS. The experimental study of matter-radiation interaction. The electromagnetic spectrum and the main spectroscopic techniques.
11. Rotational spectra of diatomic molecules. Number, arrangement and intensity of the bands. Effect of T (Boltzman distribution).
12. Vibrational spectra: insights based on the models developed in the first part. Introduction to Raman spectroscopy.
13. Electronic spectra. Franck-Condon principle and vibronic structure. Chromophores. Fluorescence and phosphorescence 

Frontal lectures with the use of the blackboard and projection of support slides.

The exam test aims at verifying the basic knowledge acquired by the student on the principles and methods of quantum mechanics and the capabilities (including critical reasoning) in applying it to the description of the structure (electronic configuration, bonds, geometry, etc.) and of the chemical-physical properties (stability, electrical properties, chemical properties, spectroscopy, etc.) of atoms and molecules.
The exam consists of written test structured in a series of open questions and numerical exercises on the teaching topics. To each question and/or exercise a partial score is assigned (in fractions of 30) that takes into account the specific difficulty, in terms of both the required knowledge and the time needed for response. The final vote is obtained by the sum of the partial scores, up to a maximum of 30/30 and Lode.
If the final mark is close to sufficience, the student will have the possibility to integrate the written exam with a short oral on the most critical topics, so to reach the sufficiency. The oral integration can be requested by the Professors when the written exam reveals serious deficiencies in some parts of the program.

Textbooks:

- P. Atkins & J. De Paula, Physical Chemistry, Oxford

Other textbooks:
- G. K. Vemulapalli, Physical Chemistry, Edises.
- D. A. McQuarrie; J. D. Simon, Physical Chemistry. A molecular approach, USB.
(Note: This text is not publlished anymore. Students can find copies of it in the chemistry library.

- Slides presented in class.

Attendance: not required, but strongly recommended.

he procedures for carrying out the lectures may change in agreement with the sanitary emergency restrictions. Anyway the online learning will be ensured for the whole year